1. Chapter 8
Section 5

2. More Simplifying and Operations with Radicals
8.5
More Simplifying and Operations with Radicals
Simplify products of radical expressions.
Use conjugates to rationalize denominators of radical expressions.
Write radical expressions with quotients in lowest terms. 2 3

3. More Simplifying and Operations with Radicals
The conditions for which a radical is in simplest form were listed in the previous section. A set of guidelines to use when you are simplifying radical expressions follows:
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4. More Simplifying and Operations with Radicals (cont’d)
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5. Simplify products of radical expressions.
Objective 1
Simplify products of radical expressions.
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6. Multiplying Radical Expressions
EXAMPLE 1
Multiplying Radical Expressions
Find each product and simplify.
Solution:
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7. Multiplying Radical Expressions (cont’d)
EXAMPLE 1
Multiplying Radical Expressions (cont’d)
Find each product and simplify.
Solution:
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8. Using Special Products with Radicals
EXAMPLE 2
Using Special Products with Radicals
Find each product. Assume that x ≥ 0.
Solution:
Remember only like radicals can be combined!
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9. Using a Special Product with Radicals.
Example 3 uses the rule for the product of the sum and difference of two terms,
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10. Using a Special Product with Radicals
EXAMPLE 3
Using a Special Product with Radicals
Find each product. Assume that
Solution:
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11. Use conjugates to rationalize denominators of radical expressions.
Objective 2
Use conjugates to rationalize denominators of radical expressions.
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12. Use conjugates to rationalize denominators of radical expressions.
The results in the previous example do not contain radicals. The pairs being multiplied are called conjugates of each other. Conjugates can be used to rationalize the denominators in more complicated quotients, such as
Using Conjugates to Rationalize a Binomial Denominator
To rationalize a binomial denominator, where at least one of those terms is a square root radical, multiply numerator and denominator by the conjugate of the denominator.
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13. Using Conjugates to Rationalize Denominators
EXAMPLE 4
Using Conjugates to Rationalize Denominators
Simplify by rationalizing each denominator. Assume that
Solution:
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14. Using Conjugates to Rationalize Denominators (cont’d)
EXAMPLE 4
Using Conjugates to Rationalize Denominators (cont’d)
Simplify by rationalizing each denominator. Assume that
Solution:
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15. Write radical expressions with quotients in lowest terms.
Objective 3
Write radical expressions with quotients in lowest terms.
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16. Writing a Radical Quotient in Lowest Terms
EXAMPLE 5
Writing a Radical Quotient in Lowest Terms
Write in lowest terms.
Solution:
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